Determine the value of x, then y, finally z.

To find the angle in the bottom triangle that is unknown, aside from x, you subtract 130 from 180 because both angles supplements each other. Then, you subtract 113 (63 + 50) from 180, giving you 67 for x.
y is 63 because of vertical angles.
z is 180 - 85 - 63 = 32.

  sides are proportional and angles are congruent

Step-by-step explanation:

Every segment in ABCDEFG is parallel to, and double the length of, the corresponding segment in HIJKLMN. All corresponding angles are congruent. Thus, the definition of similar polygons is met:

corresponding sides are angles are congruent.